The long-term objective of the proposed research is the improvement of the image quality of tomograms to aid diagnostic radiologists in the diagnosis of disease and radiation therapists in the accurate location of structures important in treatment planning for cancer therapy, etc. It is our opinion that the improvement of the image quality of tomograms will only follow the development of a new mathematical approach to describe the tomographic process. We propose to develop a new mathematical approach based on a Fourier decomposition technique widely applied in other fields. We believe this mathematical model will permit ourselves and other groups to investigate better methods of optimizing the use of present tomographic processes and equipment, suggest new procedures in forming tomographic images, and give a better framework in which to study the possibility of using image enhancement and/or pattern recognition techniques in improving the quality of the information available to the diagnostic radiologist and radiation therapist.